Reversed optimal control approach for seismic retrofitting of inelastic lateral load resisting systems

A new optimal control approach is presented for designing and controlling inelastic lateral load resisting systems. This paper uses the technique to develop a seismic retrofit procedure for inelastic shear-type resisting systems with stiffness changes and nonlinear fluid viscous dampers (FVDs). Generally, optimal control procedures aim to derive the optimal constant output feedback gains based on the weighting components assigned to the system's regulated outputs, which define their relative importance during the cost function minimization process. However, stiffness changes and FVD coefficients (the constant output feedback gains) are initially assigned in the reversed optimal control approach. Then, the consequent weighting matrices are calculated assuming the system is at its optimal state. Finally, a recurrence relation for updating the stiffness changes and added damping quantities is proposed based on the relative size between the weighting matrix components. While this paper addresses inelastic shear-type resisting systems, the reversed optimal control approach is suitable to other dynamic systems whose state vector trajectory can be determined. Two case studies examine and exemplify the developed procedure. The first case study analyzes a spectrum of single-degree-of-freedom (SDOF) systems and investigates the correlation between the weighting components and system configurations. The second case study applies the developed procedure to a five-story shear-type resisting system and demonstrates its reliability in sequentially minimizing the cost function while reducing relative interstory drifts and absorbed yield energy.